I grew up with a mutt that I loved dearly. My parents got her because my Dad had read something or other in (I think) Popular Science about how the "dog of the future" would be a mutt, and the mutting of genes would suppress bad recessive traits. Then she got sick as a puppy, had an allergic reaction to her medication, and suffered permanent brain damage. That having been said, she was a perfect house pet; lived to be a very ripe old age and was good natured, just a little slow to respond to things.
If you're a breeder and there's something wrong in the genetics of the dog you're breeding, stop breeding that dog. But resolving genetic issues isn't as simple as just throwing mutts together; you really just roll the dice on a new set of strengths and weaknesses when you do that.
Genetics are a lottery, starting with unhealthy parents the odds are against the offspring. It'll take generations for the population as a whole to move towards being healthier on average.
Of course, they are also very smart, tough, low-maintenance, and tend to live for a very long time. Some are a little over-active, but mine will happily lay in her bed all day and sleep, as long as she gets a good walk in the morning.
Living in an apartment I can't really have a big dog and by getting a breed dog (even if it's not really pure bread) I know it will not get too big for the space I have available.
Then again, it's exactly why I feel safer getting a breed dog that fits the basic requisites. In my parents home - that is quite big and with a lot of open space - we've got a mutt and we were very happy with him, but we didn't really have any constrains about how he would turn out to be as an adult.
Rescue organizations (in the US at least) are a great place to find dogs. The dogs have often been in a domestic setting with a foster owner. The history of the dog is usually known. You'll be adopting dogs in the 2-8yr range and you'll have a great idea of what you're getting.
It can take a while to find the right dog, but it should. It's a decade-long commitment.